Australian cities began easing lockdown restrictions as the country recorded a drop in community transmission of COVID-19, with only one new case reported in the last 24 hours.
"We are winning but we have not won yet," Health Minister Greg Hunt stressed.
Australia, which imposed an early shutdown of borders and businesses, has managed to reduce the number of cases and deaths.
Coronavirus testing centres have been set up across the country, with the government urging people to undergo tests regardless of whether they have symptoms.
A month after being closed for violations on social distancing rules, Bondi Beach and two neighbouring beaches in Sydney were reopened to local residents on Tuesday.
Meanwhile, New South Wales (NSW) state announced easing of stay-at-home rules.
"Two adults will be able to go and visit anybody else in their home on the basis of care, on the basis of reducing socialisation and everybody's mental health," said NSW Premier Gladys Berejiklian, with children allowed to accompany adults on house visits.
US President Donald Trump has expanded a list of countries subject to a full travel ban on Tuesday, prohibiting citizens from an additional seven countries, including passports from Syria and Palestine, from entering the United States.
The alleged gunman shot dead by police during Sunday's attack on Australia's Bondi beach was originally from the southern Indian city of Hyderabad and his family did not know about his 'radical mindset', Indian police said on Tuesday.
US President Donald Trump has ordered on Tuesday a "blockade" of all sanctioned oil tankers entering and leaving Venezuela, in Washington's latest move to increase pressure on Nicolas Maduro's government, targeting its main source of income.
The Israeli military have shot dead a 16-year-old Palestinian during a raid on the town of Tuqu' on Monday, the Palestinian health ministry said, the latest deadly incident in a recent surge of violence in the Israeli-occupied West Bank.